Apparatus for producing a distortion-free two-dimensional image of a scanned object

ABSTRACT

In a scanning device capable of building a distortion-free two-dimensional image on a surface to be scanned. The scanning operation for two directions are independently executed. Employable is a linear light source. In this case, the scanning in one direction of the two-dimensional scanning is responsive to the position of the light emitting elements in the linear light source.

BACKGROUND OF THE INVENTION

This application is a continuation of application Ser. No. 07/649,314,filed Jan. 31, 1991, now abandoned; which is a continuation of Ser. No.07/547,210 filed Jul. 3, 1990 now abandoned; which is a divisional ofSer. No. 07/288,980 filed Dec. 23, 1988, now U.S. Pat. No. 5,046,795.

This invention relates to an improvement made to a scanning device thatis capable of building a distortion-free two-dimensional image on asurface to be scanned, and more particularly to a scanning deviceconfigured to effect deflection and convergence of a light beam for thetwo scanning directions independently of each other.

Conventionally, there have been prior art systems to build an image bytwo-dimensionally scanning optical spots on a surface to be scanned, asdisclosed in Japanese Patent Publication Sho44-9321 and Japanese PatentProvisional Publication Sho51-26050.

The two-dimensional deflection devices disclosed in these documentshowever, have a problem when the angular position of one directionaldeflection is kept constant with respect to the other directionaldeflection, scanning on the surface to be scanned suffers fromdistortion, requiring a complicated and large-scale electrical system toelectrically correct the light paths for scanning.

Japanese Patent Publication Sho62-20524 and Sho62-20525 disclosearrangements to optically and mechanically eliminate such scanningdistortion. Such scanning devices are, however, configured to deflectthe light beam from a light source with a single deflector and thereforerequires a complicated dual-axis drive mechanism for the deflector. Theproblem associated with the arrangement having no independent controlmechanism for each scanning direction is described below with referenceto FIGS. 1 through 3.

The example shown here employs a polygonal mirror for deflection and aso-called fθ lens with a distortion aberration with which the imageheight "h" should be equal to a product of the incident angle "θ" by thefocal length "ƒ".

Accordingly, the image height "h" is given by

    h=ƒ·θ-(1)

In FIG. 1, numeral 10 indicates a rotationally symmetric (or spherical)fθ lens, whose optical axis coincides with the x-axis indicated by thedot-dash line.

Assuming a y-axis and a z-axis that are orthogonal to the x-axis and toeach other, the y-z plane is supposed to be the surface to be scanned.Also assuming a point at which a light beam emitted from a light sourcenot shown falls upon the reflection surface of the deflector as O₀, thelight beam appears as if it is emitted from the point O₀ as shown inFIG. 1.

In a one-dimensional scanning device to deflect the optical spots formedon the surface to be scanned only in one direction on the y-axis or thez-axis, the constant velocity of the optical spot on the surface to bescanned is ensured by the effect of the aforementioned fθ lens, whichmakes the scanning lines linear.

If, in contrast, the optical spot is to be two-dimensionally scanned inthe y-z plane, a problem is encountered as described below.

Assume that the intersection point at which the X-axis meets a virtualplane H (double-dot-dash line) perpendicular to the x-axis if O₁, whilethe intersection point at which it meets the scanning surface is O₂, andfurther that the intersection point at which the incident light beampassed by point O₀ to enter the fθ lens 10 at an angle of θ_(AX) to thex-axis meets the virtual plane H is P₁, while the intersection point atwhich it meets the surface to be scanned is P₂. The angle between thelight beam O₀ P₁ and the Z-X plane is then θ_(Y), the angle between theline segment made by reflection of the light beam O₀ P₁ on the Z-X planeand the x-axis is θ_(Z), and the angle between the line segment O₁ P₁and the Z-X plane is γ, as shown in an enlarged view of FIG. 2A. Furtherassume here that the intersection point at which the perpendicular lineP₁ to the Z-X plane meets the Z-X plane is P'₁, the equation holds:##EQU1## It also holds that where: ##EQU2## Thus, θ_(AX) and γ can berepresented by the following equations:

    θ.sub.AX =cos.sup.-1 (cos θ.sub.Y ·cos θ.sub.Z)(2)

    γ=tan.sup.-1 (tan θ.sub.Y /sin θ.sub.Z)  (3)

FIG. 2B illustrates the relationship shown in FIG. 2A, projected ontothe individual planes for easier understanding of the aboveexplanations. FIG. 2C shows a different way of representing thetriangular relationship including A_(z) for the same purpose.

As shown in FIG. 1, the angle between O₂ P₂ on the surface to be scannedand the z-axis is also γ, so O₂ P₂ is represented by the followingequation as is understood from the equation (1), where the focal lengthof the fθ lens is ƒ:

    O.sub.2 P.sub.2 =ƒ·θ.sub.AX        ( 4)

Accordingly, the coordinates of P, P (y, z) are indicated by followingequations

    Y=ƒ·θ.sub.AX ·sin γ (5)

    Z=ƒ·θ.sub.AX ·cos γ (6)

As is readily understood from the above equations (5) and (6), in suchan optical system, the value y of the Y-coordinate and the value z ofthe Z-coordinate are both functions of θ_(AX), γ so Y, Z are related toeach other by way of θ_(AX), γ. Consequently, when varying either θ_(Y)or θ_(Z), while keeping the other constant, the displacement of theoptical spot on the surface to be scanned is represented by the changein components in both Y and Z directions. In practice, curved scanninglines are produced as shown in FIG. 3. In order to minimize the curve sothat the y-coordinate can be determined by θ_(Y), and the z-coordinateby θ_(Z) independently of each other, to thereby allow the line image tobe linearly scanned, the scanning line indicated by the solid line inFIG. 3 must approximate the line indicated by the double-dot-dash line.For this purpose, the image building optical system should consist of anfθ characteristic plane satisfying an equation

    O.sub.2 P.sub.2 =ƒ·θ.sub.AX

and a correction surface with the F(γ) characteristic in operativeassociation with fθ characteristic plane, the final y and z coordinatesthereof being determined by

    Y=F.sub.Y (γ)·θ.sub.AX ·sin γ=ƒ·θ.sub.Y

    Z=F.sub.Z (γ)·θ.sub.AX ·cos γ=ƒ·θ.sub.Z

F_(Y) (γ), F_(Z) (γ): Correction function for varying the focal lengthby γ

The above conditions can be generalized so that the image height O₂ P₂is given by the above equation

    O.sub.2 P.sub.2 =ƒ·g (θ.sub.AX)

For example, an fθ lens should satisfy

    g (θ.sub.AX)=θ.sub.AX

If an arc sine lens is used, as with a galvanomirror, an equation shownbelow is satisfied ##EQU3##

xφ=Amplitude of sine oscillation of galvanomirror

In this case, the image building optical system is required to providethe characteristics satisfying the relation:

    Y=F.sub.Y (γ)·g (θ.sub.AX)·sin γ=ƒ·g (θ.sub.Y)

    Z=F.sub.Z (γ)·g (θ.sub.AX)·cos γ=ƒ·g (θ.sub.Z)

The two-dimensional scanning device disclosed in Japanese PatentPublication Sho62-20520 compensates for the scanning distortion bymechanichallly rotating the scanning lens. This is an arrangement totwo-dimensionally scan a single optical spot formed by a light beam froma point light source. Thus, it is still associated with suchdisadvantages as the upper speed limit for building a two-dimensionalimage and a complicated drive mechanism, because the deflector fordeflecting light is driven through two axes, while also driving thescanning lens at the same time. Furthermore, there is another opticalsystem proposed to simultaneously scan two optical spots by providingtwo light sources to thereby speed up the image building procedure.However, this cannot be a system of building an image by a singlescanning process in terms of its principle as well as actual effects.

SUMMARY OF THE INVENTION

It is therefore an object of the invention to provide an improvedscanning device which is capable of thoroughly optically compensatingfor the distortion of scanning lines.

Another object of the invention is to provide an improved scanningdevice which is capable of rapidly generating a two-dimensional image,by employing a one-dimensional light source instead of a point lightsource, with compensation for any distortion.

For this purpose, according to one aspect of this invention, there isprovided a scanning device for scanning a predetermined surface, whichis defined by two axes crossing each other at a right angle, with alight beam to build a two-dimensional image thereon, which comprises:

light emitting means for emitting the light beam in a predetermineddirection;

first deflecting means for deflecting the light beam emitted from thelight emitting means, on a first plane which is sectioned along one ofthe axes;

first refracting means for refracting the light beam deflected by thefirst deflecting means in such a fashion that all the principal rays ofthe light beam passed through the first refracting means become parallelto each other;

second deflecting means for deflecting the light beam deflected by thefirst deflecting means, on a second plane which is sectional along thesecond axis, the positional relationship of the second plane withrespect to the second axis along the direction of one of the axes beingdetermined depending upon the deflection angle of the principal rays atthe first deflecting means, and

second refracting means for refracting the principal rays deflected bythe second deflecting means on the predetermined surface.

According to another aspect of this invention, there is provided ascanning device for scanning a predetermined surface, which is definedby two axes crossing each other at a right angle, with a light beam tobuild a two-dimensional image thereon, which comprises:

a one-dimensional light source comprising a plurality of light emittingelements linearly arranged one upon another along one of the two axes,each of the light emitting elements emitting the light beam in apredetermined direction;

first deflecting means for deflecting the light beam emitted from therespective light emitting elements, on a first plane which is sectionedalong one of the axes,

first refracting means for refracting the light beam deflected by thefirst deflecting means in such a fashion that all the principal rays ofthe light beam passed through the first refracting means become parallelto one another;

second deflecting means for deflecting the light beam deflected by thefirst deflecting means, on a second plane which is sectioned along theother of the axes, the positional relationship of the second plane withrespect to the other of the axes along the direction of one of the axesbeing determined depending upon the deflection angle of the principalrays at the first deflecting means; and

second refracting means for refracting the principal rays deflected bythe second deflecting means on the predetermined surface.

DESCRIPTION OF THE ACCOMPANYING DRAWINGS

FIG. 1 is a general explanatory view of a two-dimensional scanningoptical system;

FIG. 2A is a partially enlarged view of FIG. 1;

FIGS. 2B and 2C are explanatory views provided for easier understandingof the relation illustrated in FIG. 2A;

FIG. 3 is an explanatory view showing distortion of scanning lines;

FIG. 4 is a perspective view showing a first embodiment of the scanningdevice according to the invention;

FIGS. 5A and 5B are exploded views taken along a light path of theoptical system shown in FIG. 4;

FIG. 6 is a perspective view showing a second embodiment of theinvention;

FIGS. 7A through 7C are exploded views taken along a light path of theoptical system shown in FIG. 6;

FIG. 8 is a perspective view showing a third embodiment of theinvention;

FIGS. 9A and 9B are exploded views taken along a light path of theoptical system shown in FIG. 8;

FIG. 10 is an explanatory view of the image building optical systemshown in FIG. 8;

FIG. 11 is a perspective view showing the shape of a correction surfaceof a compensator shown in FIG. 8;

FIGS. 12A and 12B are explanatory view showing the correction effect ofthe image building optical system shown in FIG. 8;

FIG. 13 is an exploded view taken along a light path of the opticalsystem shown in FIG. 8, without a compensator;

FIG. 14 is a perspective view showing the shape of a correction surfaceof an image building optical system shown in FIG. 8, and

FIG. 15 is an explanatory view showing a scanning line after correctionwith the image building optical system shown in FIG. 8.

DESCRIPTION OF THE EMBODIMENTS

One arrangement of the scanning device according to the inventionintends to achieve the aforementioned object by employing a point lightsource is shown in FIG. 4.

The operation of this example is described below with reference to FIGS.5A and 5B, which are exploded views taken along different planes,wherein FIG. 5A is a view exploded along an X-Y plane and FIG. 5B alonga Z-X plane.

A general explanation is given with reference to FIG. 4. A scanningdevice according to the first embodiment is provided with a point lightemitting element 10, such as a semiconductor laser. A collimator lens 11is provided to make the light fluxes from the light emitting element 10parallel.

An auxiliary polygonal mirror 15 acts as an auxiliary deflector whichdeflects the light beam emitting from the collimator lens 11 in thevertical scanning plane along the optical axis X of the collimator lens,as indicated by the dot-dash line in the drawing. The polygonal mirror15 is rotatable about a rotary axis which is perpendicular to thevertical scanning plane.

A telecentric lens 20 gathers the light beams passed through theauxiliary polygonal mirror 15 at different angles to deliver light beamsthat are parallel to the optical axis x in the vertical scanning plane,so that the light beams passed through the telecentric lens arereflected parallel to each other by another polygonal mirror 30, to bedescribed below. In the first embodiment, the telecentric lens 20 isprovided with a cylinder lens that effects refraction only in thevertical scanning plane, it being possible to use a toric lens that alsoprovides a refraction effect in the horizontal scanning plane orthogonalto the vertical scanning plane and parallel to the optical axis.

The polygonal mirror 30 behaves as a horizontal deflector. It isrotatable about a rotary axis S₂ that is perpendicular to the opticalaxis x and is parallel to the vertical scanning plane. The light beamemitting from the telecentric lens 20 in parallel with the optical axisx are reflected and deflected on plural reflection surfaces 31 inparallel with the rotary axis S₂.

Cylinder lens 40 exhibits a refraction effect only in the deflectingdirection, (i.e., only in the horizontal plane) so that the reflectedlight beam reaches a surface to be scanned 50 that is orthogonal to theoptical axis by way of the cylinder lens 40.

In this embodiment, the polygonal mirror 30 used as a deflector, and thecylinder lens 40 provides the characteristics of an fθ lens. If agalvanomirror or the like is used as a deflector, the cylinder lens 40is required to provide the characteristics of an arc sine lens. Thisrelation also holds between the auxiliary deflector 15 and thetelecentric lens 20.

The actual operation of this optical system is described with referenceto FIGS. 5A and 5B.

The light beam emitted from the light emitting element 10 is reflectedand deflected on the auxiliary polygonal mirror 15 by way of thecollimator lens 11. The resultant parallel beam runs along the x-y planeto reach the telecentric lens 20.

The light beam bearing the telecentric lens 20 is converged to a lightbeam whose distance from the optical axis x corresponds to the rotaryangle of the auxiliary polygonal mirror 15. The telecentric lens 20provides a refraction effect to build an image from each light beam onthe surface to be scanned 50 only in the x-y plane. It does not causeany refraction effect on the light beams in the z-x plane.

The light beams leaving the telecentric lens 20 are then reflected anddeflected on the reflection surfaces 31 of the polygonal mirror 30 andenters the cylinder lens 40, providing a refraction effect only in thisdeflecting direction. Since the light beams entering the reflectionsurfaces 31 are parallel to the optical axis x, and the reflectionsurfaces 31 are parallel to the y-axis, the light beams running from thereflection surfaces 31 to the surface to be scanned 50 run in the planewhich is parallel to the Z-X plane, regardless of its deflectingdirection determined by the polygonal mirror 30. Light beams emittedfrom the light emitting element 10 are converged in the y direction bymeans of the telecentric lens 20 mentioned above, and are then convergedin the z direction by means of the cylinder lens 40 so as to build anoptical spot on the surface to be scanned 50. The y coordinate of theoptical spot is determined only by the rotary angle of the auxiliarypolygonal mirror 15, while the z coordinate is determined only by therotational angle of the horizontal polygonal mirror 40.

FIG. 5A shows the position of the auxiliary polygonal mirror 15indicated by the broken line, which has been angularly moved through anangle θ_(Y/2) from the position indicated by the solid line. Assuminghere that the focal length of the telecentric lens 20 is ƒ_(Y), theimage height h_(Y) in the y direction is ƒ_(Y) ·θ_(Y), regardless of thez coordinate at the optical spot because each principal ray emitted fromthe telecentric lens 20 is parallel to each other in the x-y plane.

FIG. 5B shows the position of the plural reflection surfaces 31 of thehorizontal polygonal mirror 30, as indicated by the broken line, when ithas been angularly moved through an angle θ_(Z/2) from the positionindicated by the solid line. Assuming here that the focal length of thecylinder lens 40 is ƒ_(Z), the image height h_(Z) in z direction isƒ_(Z) ·θ_(Z), regardless of the y coordinate at the optical spot.

Consequently, with the light emitting element 10 pulsed ON-OFF inresponse to written information, a raster scan can be effected byrotating the auxiliary polygonal mirror 15 at a low speed while rotatingthe horizontal polygonal mirror 30 at a higher speed. Thus, adistortion-free, two-dimensional image can be quickly built with no needfor complicated electrical processing.

The scanning line pitch in the z direction can be arbitrarily set independence on the relative rotation of both polygonal mirrors.

When the horizontal and vertical scanning deflectors are provided by agalvanomirror, an A/O deflector or similar device, which is able tochange the deflection angle to a desired value in proportion to an inputsignal, is used together with an fθ lens. The deflection angle at eachdeflector is in a linear relation to the displacement of the opticalspot on the surface to be scanned 50, so that the vector scan operation,which has so far been difficult, is available without any complicatedcontrol.

A second embodiment of the invention, using a one-dimensional lightsource is illustrated in FIG. 6.

The scanning device in the second embodiment is provided with amultiple-spot light emitting unit 10 having a light source with linearlyarranged multiple light emitting elements such as an LED array or amulti-spot light emitting laser, and a collimator lens 11 which makesthe light beam emitted from the multi-spot light emitting unit 10parallel.

Telecentric lens 20 gathers the light beams emitted from different lightemitting elements of the multi-spot light emitting unit 10 and passedthrough the collimator lens 11 at different angles, and delivers aconvergent light beam parallel to the optical axis x of the opticalsystem, as indicated by a dot-dash line. An aperture stop 21 is placedon the objective focal plane side of the telecentric lens 20. In thisembodiment, the telecentric lens 20 is provided by a cylinder lens thateffects refraction only in the direction toward the line direction ofthe light emitting elements at the multi-spot light emitting element 10.

Polygonal mirror 30 is a horizontal deflector that is rotatable about arotary axis S that is perpendicular to the optical axis x and isparallel to the direction toward the line direction of the light emittedelements. Multiple light beams emitting from the telecentric lens 20 inparallel with the optical axis x are reflected and deflected on pluralreflection surfaces 31 formed on the sides of the polygonal mirror 30 inparallel with the rotary axis S.

A cylinder lens 40 has a refraction effect only in the deflectingdirection, so that the reflected light beams reach a surface to bescanned 50 that is orthogonal to the optical axis by way of the cylinderlens 40. In this embodiment, the polygonal mirror 30 is used as ahorizontal deflector and, the cylinder lens 40 provides the function ofan fθ lens having a distortion aberration with which the image height isequal to the product of the focal length by the incident angle. If agalvanomirror is used as a horizontal scanning deflector, thecharacteristics of the scanning lens should be changed to provide thefunction of an arc sine lens in response to its rotationalcharacteristics.

Orthogonal coordinates with a y-axis extending toward the line directionand a z-axis extending in the scanning direction are assumed in thesurface to be scanned for the purpose of explanation. An actual designexample is now described with reference to FIGS. 7A through 7C.

These drawings are views of the optical system shown in FIG. 6, takenalong the optical axis x of the optical system, wherein FIG. 7A is aview taken along the x-y plane and FIGS. 7B and 7C are views taken alongthe z-x plane.

Collimator lens 11 is a rotationally symmetric (spherical) five grouplens system comprising a planoconvex lens and meniscus lens, having afocal length of 50 mm.

Telecentric lens 20 is a rotationally unsymmetric (spherical) cylinderlens system comprising three incident lenses and one output lens, havinga focal length of 430 mm in the x-y plane.

Cylinder lens 40 comprises three rotationally unsymmetric cylinderlenses with a focal length of 300 mm in the z-x plane.

The light beams emitted from the multiple light emitting elements of amulti-spot light emitting element 10 are made parallel by passingthrough the collimator lens 11, and further extends along the x-y planeto reach the aperture stop 21 by way of the telecentric lens 20.

The light beams emitting from the telecentric lens 20 are convergentfluxes, whose distance h_(Y) from the optical axis x is proportional tothe distance h_(Y) ' between the optical axis x and its light beam,i.e., the light emitting element. The telecentric lens 20 provides arefraction effect to build an image from each light beam on the surfaceto be scanned only in the x-y plane. It does not cause any refractioneffect on the light beams in the z-x plane.

The light beams emitted from the telecentric lens 20 are then reflectedand deflected on the reflection surfaces 31 of the polygonal mirror 30and enters the cylinder lens 40, providing a refraction effect on thisdeflecting direction. Since the light beams entering the reflectionsurfaces 31 are parallel to the optical axis x, and the reflectionsurfaces 31 are parallel to the y-axis, the light beams running from thereflection surfaces to the surface to be scanned 50 run in the planewhich is parallel to the Z-X plane and whose distance from the Z-X planeis h_(Y).

Light beams emitted from the light emitting elements are converged inthe y direction by means of the telecentric lens 20 mentioned above, andare then converged in the z direction by means of the cylinder lens 40to build separate optical spots on the surface to be scanned 50. The ycoordinate of the optical spot is determined only by the light emittingposition h_(Y) ' of the multi-spot light emitting element 10, while itsz coordinate is determined exclusively by the rotational angle of thepolygonal mirror 30.

FIG. 7C shows the position of the polygonal mirror 30 which has beenangularly moved through an angle θ_(Z/2) from the position shown in FIG.7B. Assuming, for example, that θ=4.5° here, the image height h_(Z) inthe z direction is: h_(Z) =47 mm, independently of the coordinate in ydirection.

Consequently, when the polygonal mirror 30 is kept stationary, lineimages parallel to the y axis can be built on the surface to be scanned50 by turning on the light emitting elements. If, on the other hand, thepolygonal mirror 30 is rotated while driving the light emitting elementsseparately, a two dimensional image corresponding to the number of thelight emitting elements can be built by a single mechanical scanningoperation, i.e. the rotation of the polygonal mirror 30.

Since the y-z coordinates on the surface to be scanned 50 can thereforebe controlled independently of each other, a distortion-freetwo-dimensional image can be quickly built with no need for complicatedelectrical processing.

A third embodiment of the invention, employing a one-dimensional lightsource, is described below with reference to the drawings.

First, a general explanation is given with reference to FIG. 8. A lineimage scanning device comprises a one-dimensional light source 10 withmultiple light emitting elements provided in a row, such as an LED arrayor a multi-spot light emitting laser unit, a polygonal mirror 30 thatoperates as a deflector that is rotatable about a rotary axis S to scanthe light beam emitted from the one-dimensional light source 10, and animage building optical system 46 having its optical axis x within thescanning plane perpendicular to the rotary axis. A collimator lens 55 isprovided between the one-dimensional light source 10 and the polygonalmirror 30. As in FIG. 1, a y-axis orthogonal to the x-axis and parallelto the rotary axis S, and a z-axis orthogonal to the x and y axes areassumed for the purpose of explanation, with the y-z plane set as asurface to be scanned.

FIGS. 9A and 9B are exploded views of the optical system shown in FIG.8, along the light path, wherein FIG. 9A is a view taken along the x-yplane and FIG. 9B is a view taken along the z-x plane.

The light beams emitted from the one-dimensional light source 10 reachesthe reflection surfaces 31 of the polygonal mirror 30 by way of thecollimator lens 55. It is then reflected and deflected on the reflectionsurfaces 31 so that a line image representative of the light emittingpattern of the one-dimensional light source 10 is built on the surfaceto be scanned by means of the image building optical system 46.

Since the light beams emitted from the light emitting elements of theone-dimensional light source 10 generate separate optical spots on thesurface to be scanned 50, the scanning lines corresponding to the numberof the light emitting elements are provided by a single scanningoperation. Consequently, a two-dimensional image is obtained by only asingle scanning operation by separately driving the light emittingelements of the one-dimensional light source 10.

The image optical system 46 shown in this example comprises an fθ lenssystem 44 having three rotationally symmetrical lenses 41, 42 and 43(FIG. 10) satisfying an eqnation

    ƒ.sub.Y =ƒ.sub.Z =ƒ

where ƒ_(Y) is a focal length of the line image sectional area and ƒ_(Z)is a focal length within the deflecting sectional area. A compensator 45is provided with a rotationally unsymmetric correction surface 45a (FIG.9B).

The surface configuration of the fθ lens system 44, and the generalarrangement of the image building optical system 46 are as illustratedin FIG. 10 and in

                  TABLE 1                                                         ______________________________________                                        FOCAL DISTANCE  f = 99.98                                                                                REFRACTIVE                                         CURVATURE       DISTANCE   INDEX                                              ______________________________________                                        fθ LENS                                                                         r.sub.1                                                                             -18.980                                                         (44)                    d.sub.1                                                                            3.09  n.sub.1                                                                            1.5107                                        r.sub.2                                                                              ∞                                                                                d.sub.2                                                                            1.32                                                     r.sub.3                                                                             -201.738                                                                                d.sub.3                                                                            6.36  n.sub.2                                                                            1.6145                                        r.sub.4                                                                             -31.514                                                                                 d.sub.4                                                                            1.18                                                     r.sub.5                                                                             ∞                                                                                 d.sub.5                                                                            4.64  n.sub.3                                                                            1.5107                                        r.sub.6                                                                             -37.980                                                                                 d.sub.6                                                                            5.0                                              COMPENSATOR (45)                                                                              d.sub.7                                                                              3.0     n.sub.4                                                                            1.5107                                    ______________________________________                                    

The correction surface 45a is generally shaped as indicated in FIG. 11so that it forms a gently curved cylindrical surface in terms of the ydirection, whose four corners are slightly raised, with its center inthe y direction slightly recessed. Specific surface configurations areshown in Table 2. This table shows the x-coordinate (unit: μm) of apoint determined by the y and z coordinates (unit: mm), assuming thatthe intersection at which the optical axis x of the fθ lens sysytem 44meets the correction surface 45a is a zero point (0, 0, 0). Since thecorrection surface 45a is symmetrical with respect to the y and z axes,y and z coordinates are represented by + and - at the same time.

                  TABLE 2                                                         ______________________________________                                        y    0      ±2  ±4                                                                              ±6 ±8                                                                          ±10  ±12                                                                         ±14  ±16                        ______________________________________                                        0    0      -6     -24  -55-97 -151 -213                                                                              -274 -308                             ±2                                                                              +1     -5     -24  -54-97 -151 -212                                                                              -272 -305                             ±4                                                                              +3     -3     -22  -53-95 -149 -209                                                                              -267 -298                             ±6                                                                              +6     0      -19  -50-93 -147 -207                                                                              -263 -294                             ±8                                                                              +12    +6     -14  -47-91 -146 -206                                                                              -265 -299                             ±10                                                                             +20    +13    -8   -43-90 -147 -212                                                                              -276 -323                             ±12                                                                             +29    +21    -2   -39-89 -152 -223                                                                              -300 -372                             ±14                                                                             +34    +26    +2   -37-91 -157 -237                                                                              -331 -439                             ±16                                                                             +25    +17    -6   -43-93 -157 -238                                                                              -346 -496                             ±18                                                                             -25    -30    -44  -67-97 -138 -198                                                                              -298 -495                             ______________________________________                                    

Unit of Measurement

x coordinate=μm

y coordinate=mm

z coordinate=mm

Here, the angle between the light beam emitted from one light emittingelement of the one-dimensional light source 10 and reflected on thereflection surface 31, and the Z-X plane is assumed to be θ_(Y), and theangle between the same light beam projected to the Z-X plane and thex-axis to be θ_(Z) (see FIG. 2B).

The image building optical system provides such characteristics that alight beam having an angle θ_(Y) within the line image sectional area,while making an angle θ_(Z) to the optical axis of the image buildingoptical system within the deflecting sectional area, builds an image ata location to hold equations

    Y=ƒ·θ.sub.Y

    Z=ƒ·θ.sub.Z

for arbitrary values of θ_(Y) and θ_(Z).

The incident angle θ_(Z) in the deflecting direction varies by twice thechange in the rotary angle of the polygonal mirror 30.

The incident angle θ_(Y) toward the line image is determined by thelocation h_(Y) on the line direction and the characteristics of thecollimator lens 55. In this example, the collimator lens 55 providesthat

    h.sub.Y =ƒ.sub.C ·θ.sub.Y

(where ƒ_(C) is a focal length of the collimator lens), or

    θ.sub.Y =h.sub.Y /ƒ.sub.C

As for the image building optical system 46, the location h_(Y) on theline image is made to linearly correspond to the y coordinate on thesurface to be scanned.

FIG. 12A shown the scanning characteristics provided when thecompensator 45 is excluded from the optical system as above, in themanner similar to FIG. 3, while FIG. 12B shows the scanningcharacteristics when the compensator is inserted. As is seen in FIG.12B, by inserting the compensator 45, the line image can be scannedsubstantially linearly so that it can be controlled in response to thevariation of θ_(Y) and θ_(Z) separately for y direction and z direction,the former being dependent on the light emitting position of the source10 and the latter being dependent on the rotation of the polygonalmirror 30. Thus, a distortion free two-dimensional image is built withno need for complicated electrical processing.

FIG. 13 shows an arrangement to provide the same effect withoutemploying the compensator 45 in the embodiment described above. In thisarrangement, a correction surface 43a is provided by an inner surface ofthe lens 43 as a component of the fθ lens system 44 in the imagebuilding optical system 46. FIG. 14 illustrates the surfaceconfiguration of the correction surface 43a in the same format shown inFIG. 11, with specific details given in Table 3. Table 3 can beinterpreted in the same manner as for Table 2. FIG. 15 shows thecorrection effect in the same format as shown in FIG. 12B.

                  TABLE 3                                                         ______________________________________                                        y     0      ±2   ±4                                                                              ±6 ±8 ±10 ±12                           ______________________________________                                        0     0      -9      -37  -83   -143  -210   -265                             ±2 +1     -8      -37  -82   -142  -209   -264                             ±4 +5     -5      -34  -80   -140  -208   -265                             ±6 +11    +1      -29  -76   -138  -208   -270                             ±8 +20    +9      -22  -72   -138  -212   -285                             ±10                                                                              +28    +17     -17  -70   -139  -221   -312                             ±12                                                                              +27    +15     -19  -72   -143  -230   -342                             ±14                                                                              -10    -20     -48  -91   -148  -223   -341                             ______________________________________                                    

While the focal lengths and the transformation functions (g_(Y), g_(Z))with the image building optical system 46 are assumed to be equal forthe y and z directions, the focal lengths and transformation functionsmay be different, so long as a constant pitch is maintained for eachdirection.

Accordingly, the focal lengths and transformation functions aregenerally different between the y and z direction, so that the equationshold

    Y=F.sub.Y (γ)·g.sub.Y (θ.sub.AX) sin γ=ƒ.sub.Y ·g.sub.Y (θ.sub.Y)

    Z=F.sub.Z (γ)·g.sub.Z (θ.sub.AX) cos γ=ƒ.sub.Z ·g.sub.Z (θ.sub.Z)

Linearity of the scanning lines on the surface to be scanned isguaranteed on condition that this relation is maintained.

As fully described above, the scanning device according to the presentinvention is capable of building a distortion-free two-dimensional imagewithout any complicated electrical processing. Further, by employing aone-dimensional light source (as a light source with a multi-spot lightemitting element), a two-dimensional image can be produced by a singlemechanical scanning operation. Therefore a two-dimensional image can berapidly produced with compensation for the distortion.

What is claimed is:
 1. An optical device for scanning a predeterminedsurface, said surface being defined by first and second axes which arepositioned perpendicularly with respect to each other, said device beingadapted to create a two-dimensional image on said surface andcomprising:light emitting means including a plurality of light emittingelements that are linearly arranged parallel to said first axis, each ofsaid light emitting elements emitting a light beam in a predetermineddirection and the light beam being directed toward a desired directionon a first plane which is sectioned parallel to said first axis; firstrefracting means for refracting each said light beam emitted from saidlight emitting means in such a fashion that all of said light beamsbecome parallel to one another; means for deflecting each said lightbeam refracted by said first refracting means, along second planes whichhave their sections located parallel to said second axis, the positionalrelationship of said second planes with respect to said second axis,along the direction of said first axis, being determined based uponrespective directions along which each said beam is emitted from saidlight emitting means; and second refracting means for refracting eachsaid beam deflected by said deflecting means on said predeterminedsurface.
 2. The optical device of claim 1, wherein said light emittingmeans further includes a collimator lens for refracting the light beamemitted from each of said light emitting elements and said firstrefracting means comprises a cylindrical lens, both lenses beingdesigned and arranged in such a fashion that said beams passed throughsaid collimator lens and said cylindrical lens become parallel to oneanother and so that the intervals between adjacent beams become enlargedafter passing through said collimator lens and said cylindrical lens. 3.The optical device of claim 2, wherein said deflecting means comprises apolygonal mirror, and said second refracting means comprises a secondcylindrical lens.
 4. The optical device of claim 3, wherein saidcollimator lens comprises a spherical five group lens system having aplanoconvex lens and a meniscus lens, said cylindrical lens being aspherical lens system comprising three incident lenses and one outputlens, said second cylindrical lens comprising a spherical three grouplens system.